refactor(ManualBackupStep2): migrate to design system components (#27577)

# PR Title

refactor(ManualBackupStep2): migrate to design system components

---

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## **Description**

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also include relevant motivation and context. Have in mind the following
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This refactor migrates `ManualBackupStep2` (SRP verification quiz) to
design system primitives and Tailwind utilities to align with current
mobile UI standards and reduce legacy styling patterns.

The screen now uses `Box`/design-system layout patterns and
`useTailwind`-based styling instead of `View` + `StyleSheet.create`,
while preserving the SRP placement flow and analytics behavior. Minor
safety improvements were included in interaction logic (e.g., radix-safe
`parseInt`, defensive array cloning before `sort`) to avoid
mutation-related edge cases.

## **Changelog**

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CHANGELOG entry: null

## **Related issues**

Fixes:

## **Manual testing steps**

```gherkin
Feature: Secret Recovery Phrase verification screen refactor

  Scenario: user completes SRP word verification in onboarding flow
    Given the user creates a new wallet and reaches the SRP backup flow
    And the app is on ManualBackupStep2

    When user taps missing words in the correct order and fills all empty slots
    Then the Continue button becomes enabled
    And user can continue to the next backup step without visual/layout regressions

  Scenario: user changes a previously selected SRP word
    Given the app is on ManualBackupStep2 with at least one filled slot

    When user taps a filled slot or taps an already-used word
    Then the previously assigned word is removed from that position
    And the slot selection/focus updates correctly for the next word tap
```

## **Screenshots/Recordings**

<!-- If applicable, add screenshots and/or recordings to visualize the
before and after of your change. -->

| Theme | Before | After |
| --- | --- | --- |
| Light | <img width="220" alt="Before light"
src="https://github.com/user-attachments/assets/ba5ebd94-e1b3-403e-86d3-b9c4b7331eb7"
/> | <img width="220" alt="After light"
src="https://github.com/user-attachments/assets/2464cf3b-2eb0-4be8-bf6f-516cdeacc19c"
/> |
| Dark | <img width="220" alt="Before dark"
src="https://github.com/user-attachments/assets/3a880168-3630-4f6b-a1b8-a9af33a357c5"
/> | <img width="220" alt="After dark"
src="https://github.com/user-attachments/assets/562e3dc8-af1b-442c-90f9-f0b5f1ea3155"
/> |

## **Pre-merge author checklist**

- [x] I've followed [MetaMask Contributor
Docs](https://github.com/MetaMask/contributor-docs) and [MetaMask Mobile
Coding
Standards](https://github.com/MetaMask/metamask-mobile/blob/main/.github/guidelines/CODING_GUIDELINES.md).
- [x] I've completed the PR template to the best of my ability
- [x] I've included tests if applicable
- [x] I've documented my code using [JSDoc](https://jsdoc.app/) format
if applicable
- [x] I've applied the right labels on the PR (see [labeling
guidelines](https://github.com/MetaMask/metamask-mobile/blob/main/.github/guidelines/LABELING_GUIDELINES.md)).
Not required for external contributors.

## **Pre-merge reviewer checklist**

- [ ] I've manually tested the PR (e.g. pull and build branch, run the
app, test code being changed).
- [ ] I confirm that this PR addresses all acceptance criteria described
in the ticket it closes and includes the necessary testing evidence such
as recordings and or screenshots.

<!-- Generated with the help of the pr-description AI skill -->

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> **Medium Risk**
> Mostly a UI/styling refactor of the SRP verification screen, but it
touches a critical onboarding flow and slightly adjusts slot/word
selection logic (sorting and index parsing), so regressions could block
SRP confirmation.
> 
> **Overview**
> Refactors `ManualBackupStep2` (SRP verification) to use design-system
primitives (`Box`, `Text`, `Icon`) and Tailwind-based styling, replacing
the legacy `StyleSheet` implementation and removing `styles.ts`.
> 
> Makes small safety/behavior tweaks in the word-placement logic (avoid
in-place `sort` mutation, use radix-safe `parseInt`, and update layout
sizing via `useWindowDimensions`/platform-specific spacing) while
keeping navigation, analytics, and success/error handling flows intact.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
5b562a6. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Author: tylerc-consensys